Adding IK Problems - shin/forearm sticks out, doesn't follow IK
The points shown in the images are full bones as normally appear, just they're very small, and not joined together (attached) as they'd usually be. The bones being small like this caused problems for the IK, allowing it to animate the position, but unable to find the 'head' and 'tail' points correctly because of their separation.
The option was to adjust the bones in edit mode so they'd join up, but doing this broke all the animations.
In the end, I simply clicked the 'tail' of one bone and the 'head' of the next, and used 'Fill' to create a new bone to connect them up. I did this for all the necessary places, so there were no 'floating' bones.
Then, I applied the IK using the newly-added bones. The original bones were kept but parented so that the new bone was a child of the original, allowing the original animations to work.
Furthermore, the weight painting had to be swapped out so that the new bones took over from the old bones as the ones which have the actual control over the body (done by simply renaming the names to math the names of the new bones). This allows the original animations to be kept, and for an IK.